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Polar coordinate identities

There’s a few things that we can say are true when working with polar coordinates - identities.

They’re really useful especially later on, when we’ll use them to convert from polar forms to cartesian forms, and the other way round.

We know this because , and in this case the adjacent side is and the hypotenuse is .

So , and rearranging gives us .

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We know this one because , and in this case the opposite side is and the hypotenuse is . So , and rearranging gives us .

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  • We can rewrite this one to if absolutely required.

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  • We can rearrange this as either of:

We do also need to check which quadrant it is in, to decide on what becomes negative in the polar coordinates.